1.

Consider an arithmetic progression with n terms. If the common difference is increased by 1, then nth term increases by 19. If the 5th term of the progression is 28 and the average of the first and last terms is 61, then the 10th term of the progression is:

Answer»
Let the A.P be
=a+(n-1)d

common difference increased by 1
a+(n-1)d+1

a+(n-1)d+19=a+(n-1)d+1
a+dn-d+19=a+dn-d+n-1
19=n-1
n=20

5th term 
a+4d=28
a=28-4d---------1

a+a+(20-1)d=122
a+a+19d=122.       ---61×2
from--1
d=6
a=4

10th term=4+(10-1)6=58


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